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[AMPS] Re: conjugate match

To: <amps@contesting.com>
Subject: [AMPS] Re: conjugate match
From: w8jitom@worldnet.att.net (Tom Rauch (W8JI))
Date: Sun, 09 Mar 1997 09:47:58 -0500
"Dick Green". wrote:

> I had a lot of trouble finding any kind of definitive answer to this
> question. Orr's Handbook points out (on p 21-4) that if the generator's
> output impedance just happens to be the same as the characteristic
> impedance of the transmission line (say, 50 ohms looking into 50 ohm coax),
> and there is a mismatch between the line and the antenna, then the
> generator will absorb all of the reflected power. I imagine this would
> cause the plates to get hot, but I don't know. Does anybody out there know?
> (Note: when the generator's output impedance, the transmission line's
> characteristic impedance, and the load impedance are all the same, say 50
> ohms, you have a "conjugate match".)
 
Orr's statement is incorrect. This is a topic many amateur texts get
wrong. The only person who wrote anything for amateur texts that has it
all correct is Walt Maxwell, in his book Reflections. The ARRL USED to
use Walt's description, but stopped lately because they have a new and
incorrect theory.

A conjugate match is when the source appears as the complex conjugate of
the load presented at the generator's output port. The complex conjugate
is the same resistive part, and the opposite reactance sign and but same
amount. If your rig feeds into a line that looks like 100 ohms with 300
ohms of parallel capacitance, and you tune for maximum power with a
fixed amount of drive, the output impedance looking back ino the rig is
100 ohms with 300 ohms of parallel inductance.

In that case NONE of the reflected power makes it back into the rig! The
rig operates normally.

That is why solid state rigs, that you can not tune, are affected by
SWR. They have no tuning controls and can NOT be adjusted to a new
conjugate match.

By the way, output impedance of any linear PA is always higher than the
load impedance. Otherwise the PA will flat top and be non-linear. That
includes transistors. 

The only PA's that are conjugately matched are those operating at
maximum power output.  
If the generator's output terminal impedance is the complex conjugate of
the load, there is a reflection at the source that compensates the line
reflection perfectly and the generator operates with maximum power
transfer (and usually very close to maximum efficiency).

> But, in most tube amp circuits, the output impedance is higher, at least
> 100 to 600 ohms.

That is another untrue statement that has crept into our Handbooks. It
is completely false to define a resistance. The stuff about solid state
PA's having LESS than 50 ohms source impedance is false also.

I started to answer the rest of your questions and comments, but after
45 minutes of typing I realized it was too long to post, and no one
would read it or understand it because it jumped around from point to
point and covered 26 topics. 

I think it's tough to learn that way, or be clearly understood.

The most common mistake is thinking the tube (or other output device,
like a transistor) is a SOURCE. It is not the source. Batteries are
sources, the wall outlet is a source, the power supply is a source (that
runs from another source, the outlet). 

The tube is a resistance that varies with time. It can NOT source
anything, it only acts like a variable resistor. We control its'
resistance with the exciter.

The tank is an "impedance" that is effectively in series with the power
source and the tube resistance.

The tank impedance controls one leg of the divider, the tube the other.
When you upset the load the tube might get hotter (if the tank impedance
becomes low), or less hot (if the tank impedance becomes high)!

One of the problems with the "new" ARRL theory is they try to apply a
Thevinin or Norton equivalent to a tube, and use it to explain conjugate
matching. The theorums themselves do NOT apply to non-linear systems,
and the tube with its time varying resistance (besides conducting for
less than 360 degrees) is NOT a linear system. It is a changing system.

In the non-linear part of a system (this is defined as a system with
either less than 360 degrees conduction or a time-varying resistance-
the tube is BOTH), we can NOT apply Thevenin, Norton, OR conjugate match
and reflected wave theorums. We have to treat the system by circuit
analysis.

The effect of reflected waves STOPS at the tank circuit (everything past
the tank is a linear constant impedance because the tank is a "flywheel"
or energy smoothing system).
Applying reflected power PAST the tank or output harmonic filter (in a
solid state PA) is totally incorrect. When Mr. Thevenin wrote his
theorum he plainly said so. Somehow the handbooks have forgotten to read
the text of the rules they quote.

So reflected power does NOT go back to the tube. Besides that, it is
only a concept or theory. It is one way to look at and simplify a
complex problem. The rules of reflected power no longer work in
non-linear systems so they do NOT and can NOT be applied at the tube or
transistor.

Circuit theory works for both the transmission line, and at the tube.
Conjugate matching only works in the case of a non-time varying
impedance, or from the tank OUT to the antenna. 

Circuit theory is more complex, so antenna and linear system (by this I
don't mean "linear" amplifier systems. I mean any system where
resistance and impedance is constant with time) engineers use conjugate
matching and reflected waves as a "tool" to simplify their calculations.
     
We always need to remember these rules, and that the tube is NOT a
source, or we will get confused. Tools are good, but they can be
misused. Don't use a wrench to pound nails.

73 Tom



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